A371421 Numbers whose aliquot-like sequence based on the largest aliquot divisor of the sum of divisors of n (A371418) terminates in a fixed point.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 67, 68, 71, 73, 74, 79, 80, 81, 82, 89, 93, 96, 97, 98, 100, 101

Offset: 1

Author

Amiram Eldar, Mar 23 2024

Keywords

• nonn

Comments

It is unknown whether 222 is a term of this sequence or not (see A371423).

Examples

			3 is a term because when we start with 3 and repeatedly apply the mapping x -> A371418(x), we get the sequence 3, 2, 1, 1, 1, ...
40 is a term because when we start with 40 and repeatedly apply the mapping x -> A371418(x), we get the sequence 40, 45, 39, 28, 28, 28, ...
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..113
• Robert D. Carmichael, Empirical Results in the Theory of Numbers, The Mathematics Teacher, Vol. 14, No. 6 (1921), pp. 305-310; alternative link. See p. 309.

Crossrefs

Cf. A371418, A371422, A371423.

A023194 is a subsequence.

Cf. A063769, A080907.

Programs

Mathematica

r[n_] := n/FactorInteger[n][[1, 1]]; f[n_] := r[DivisorSigma[1, n]]; q[n_] := Module[{m = NestWhileList[f, n, UnsameQ, All][[-1]]}, f[m] == m]; Select[Range[221], q]